I'd be much more impressed by an experiment showing that subjects spontaneously try to hurt others.

Actually,
there are plenty of those in the experimental public goods literature.
The questions raised by these public goods experiments might be what
started the "money burning" experiments.

In a
typical public goods game, four or five people are each given a little
money, and then they individually decide whether to put some of that
money in a pot. The money in the pot doubles, and then all the money in
the pot gets divided up among the four or five players (numbers are
just representative, of course). If you're only playing this game once,
the homo economicus thing to do is contribute nothing--you should just free-ride.

However,
in actual experiments, people contribute about 40 to 60 percent of
their initial endowment; Nobelist Elinor Ostrom sums up the findings in a
non-technical paper here (PDF).
If the same players repeat the game for a while, contributions drop
off. So in this context, typical people aren't narrow materialists, but
they aren't saints either.

This experimental
literature went in a lot of directions, but one matters for us: Some
economists added a chance for players to punish other players by taking
away their money (usually at a cost to the punisher). The thought was
that if people suspected they'd be punished if they didn't contribute,
they'd contribute more. And of course, that's just what happened.

But something awful happened too:
Some players punished people who were highly cooperative! So here was a
power that--to any casual observer--was specifically designed by the
experimenter to punish the wicked.

What did a substantial number of players do with that power? They punished the saints. Given a chance to spur cooperation, they "spontaneously [tried] to hurt others."

Cinyabuguma/Page/Putterman call this "perverse punishment". Here's what they found:

In
our own estimates, typically 20% or more of all punishment events are
directed at the highest contributor in the group (or highest
contributors if there are ties).

The saints must be taught a lesson.

Herrmann/Thöni/Gächter ran these kinds of games across 18 societies.
In the median society, the ratio of non-perverse to perverse
punishment looks like it's about 3:1. Perverse punishment is not rare.

So,
what kind of evil is this? The money-burning literature helps to
answer that question. If the vast majority of people had at least a little bit
of empathy, then when they saw a person who lost money through no fault
of her own, they would be reluctant to hurt that person. As the saying
goes, you don't kick a man while he's down.

What happens in experiments when nature (or a random draw of cards) destroys part of the wealth of a fellow test subject?

In "The Pleasure of Being Nasty,"
experimenters had two test conditions: One where all suffering was
inflicted by the players, and a second where part of the suffering was
inflicted by a random card draw. In the second condition, players
punished each other much more, in each and every round of the game.